Question: Which decimal is equivalent to $\dfrac{31}{9}$ ? Choose 1 answer: Choose 1 answer: (Choice A) A $0.\overline{4}$ (Choice B) B $0.4444$ (Choice C) C $3.\overline{4}$ (Choice D) D $3.4444$
Solution: $ \dfrac{31}{9}$ represents $31 \div 9 $. ${9}$ ${3}$ ${1}$ ${0}$ $\text{How many times does }9\text{ go into }{31}\text{?}$ ${3}$ ${2}$ ${7}$ $-$ ${4}$ ${31}\div9={3}\text{ with a remainder of }{4}$ ${0}$ ${.}$ ${.}$ $\text{Write in a decimal and a zero.}$ $\text{How many times does }9\text{ go into }{40}\text{?}$ ${0}$ ${0}$ ${4}$ ${3}$ ${6}$ $-$ ${4}$ ${40}\div9={4}\text{ with a remainder of }{4}$ $\text{How many times does }9\text{ go into }{40}\text{?}$ ${0}$ ${0}$ ${4}$ ${3}$ ${6}$ $-$ ${4}$ ${40}\div9={4}\text{ with a remainder of }{4}$ $\text{How many times does }9\text{ go into }{40}\text{?}$ ${0}$ ${0}$ ${4}$ ${3}$ ${6}$ $-$ ${4}$ ${40}\div9={4}\text{ with a remainder of }{4}$ $\text{How many times does }9\text{ go into }{40}\text{?}$ ${0}$ ${0}$ ${4}$ ${0}$ Notice how the decimal is repeating and will continue to repeat as we bring down more zeros. So $\dfrac{31}{9}$ is equivalent to $3.\overline{4}$.